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* feat: add MathJax option * docs: move math engine note * refactor: update LaTeX documentation and improve MathJax integration - Adjusted LaTeX documentation for clarity and formatting. - Enhanced MathJax configuration in the templates to support both KaTeX and MathJax rendering. - Removed deprecated comments and streamlined the script loading process for MathJax. - Updated the passthrough extension settings in the Hugo configuration for better compatibility with LaTeX math expressions. * docs: simplify LaTeX documentation and clarify configuration steps - Updated LaTeX documentation to reflect that KaTeX is enabled by default, removing the need for manual activation. - Added examples for using LaTeX math expressions and clarified the configuration for the passthrough extension in Hugo. - Enhanced MathJax section to emphasize its use as an alternative rendering engine.
111 lines
2.6 KiB
Markdown
111 lines
2.6 KiB
Markdown
---
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title: "数学公式"
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weight: 4
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math: true
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---
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默认情况下，\(\KaTeX\) 用于渲染 LaTeX 数学表达式。
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无需手动激活，您可以直接在 Markdown 内容中开始使用 LaTeX 数学表达式。
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## 示例
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Markdown 内容中支持内联和独立段落的 LaTeX 数学表达式。
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### 内联
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```markdown {filename="page.md"}
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这个 \(\sigma(z) = \frac{1}{1 + e^{-z}}\) 是内联的。
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```
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这个 \(\sigma(z) = \frac{1}{1 + e^{-z}}\) 是内联的。
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### 独立段落
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```markdown {filename="page.md"}
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$$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t} \, dt$$
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```
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将渲染为：
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$$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-j\omega t} \, dt$$
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例如，使用对齐环境：
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```latex {filename="page.md"}
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$$
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\begin{aligned}
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\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
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\nabla \cdot \mathbf{B} &= 0 \\
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\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
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\nabla \times \mathbf{B} &= \mu_0 \left( \mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)
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\end{aligned}
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$$
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```
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将渲染为：
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$$
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\begin{aligned}
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\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
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\nabla \cdot \mathbf{B} &= 0 \\
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\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
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\nabla \times \mathbf{B} &= \mu_0 \left( \mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)
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\end{aligned}
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$$
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## 配置
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> [!IMPORTANT]
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> 请在 Hugo 配置文件中启用并配置 [passthrough 扩展](https://gohugo.io/content-management/mathematics/)，以便 Hugo 可以检测 Markdown 内容中的 LaTeX 数学表达式。
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```yaml {filename="hugo.yaml"}
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markup:
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goldmark:
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extensions:
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passthrough:
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delimiters:
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block: [['\[', '\]'], ["$$", "$$"]]
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inline: [['\(', '\)']]
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enable: true
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```
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## 支持的函数
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有关支持的函数列表，请参阅 [KaTeX 支持的函数](https://katex.org/docs/supported.html)。
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## 化学
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通过 [mhchem](https://mhchem.github.io/MathJax-mhchem/) 扩展支持化学表达式。
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内联：\(\ce{H2O}\) 是水。
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独立段落：
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```markdown {filename="page.md"}
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$$\ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-}$$
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```
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将渲染为：
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$$\ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-}$$
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## 数学引擎
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### MathJax
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默认情况下，使用 [KaTeX][katex] 在构建过程中渲染 LaTeX 数学表达式，这是首选方式。
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或者，您可以使用 [MathJax][mathjax] 来渲染数学表达式。
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要使用 MathJax，请将以下内容添加到 `hugo.yaml` 配置文件中：
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```yaml {filename="hugo.yaml"}
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params:
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math:
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engine: mathjax
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```
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[katex]: https://katex.org/
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[mathjax]: https://www.mathjax.org/
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